Details

sample468.0ms

Algorithm

intervals

Results

135.0ms	60×	body	2560	valid
44.0ms	83×	body	1280	valid
18.0ms	60×	body	640	valid
5.0ms	30×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	13×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.6b	(- x (tan x))
0.6b	(- x (sin x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

24.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series176.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
60.0ms	(- x (tan x))
40.0ms	(- x (sin x))

simplify158.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	684
2	4781	684
3	5001	684

prune186.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
16.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series113.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 9/40 (pow x 2))
48.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify45.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	316
2	5001	313

prune138.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	74	5	79

Merged error: 0.0b

Counts

79 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
16.3b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

5.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
4.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series169.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 27/2800 (pow x 4))
27.0ms	(* 9/40 (pow x 2))
105.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify44.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	249	308
1	1003	278
2	5001	273

prune131.0ms

Filtered

73 candidates to 45 candidates (61.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	73	5	78

Merged error: 0.0b

Counts

78 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- x (tan x)) 3)
0.6b	(- x (tan x))
0.6b	(- x (sin x))
20.3b	(cbrt (pow (- x (tan x)) 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`add-log-exp`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 84

Calls

4 calls:

5.0ms	(pow (- x (tan x)) 3)
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))
5.0ms	(cbrt (pow (- x (tan x)) 3))

series214.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (- x (tan x)) 3)
54.0ms	(- x (tan x))
31.0ms	(- x (sin x))
69.0ms	(cbrt (pow (- x (tan x)) 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	352	506
1	1243	480
2	5001	474

prune181.0ms

Filtered

96 candidates to 57 candidates (59.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	96	5	101

Merged error: 0.0b

Counts

101 → 5

regimes65.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch71.0ms

Steps

Iters	Range		Point
10	1.4358440906352691e-08	58326792.95653587	0.02968012863964934
7	-0.42296476227477825	-0.006911778759371886	-0.02929154713524706

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.8s	1584×	body	2560	valid
1.6s	2775×	body	1280	valid
503.0ms	1905×	body	640	valid
159.0ms	936×	body	320	valid
52.0ms	421×	body	160	valid
28.0ms	379×	body	80	valid

Details

sample468.0ms

simplify12.0ms

prune4.0ms

localize11.0ms

rewrite38.0ms

series176.0ms

simplify158.0ms

prune186.0ms

localize10.0ms

rewrite20.0ms

series113.0ms

simplify45.0ms

prune138.0ms

localize10.0ms

rewrite17.0ms

series169.0ms

simplify44.0ms

prune131.0ms

localize12.0ms

rewrite20.0ms

series214.0ms

simplify43.0ms

prune181.0ms

regimes65.0ms

bsearch71.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling